Applications of Atiyah¿Hirzebruch spectral sequences for motivic cobordism

• Autores: Nobuaki Yagita
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 90, Nº 3, 2005, págs. 783-816
• Idioma: inglés
• DOI: 10.1112/s0024611504015084
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• Resumen

  • In this paper, we study applications of Atiyah¿Hirzebruch spectral sequences for motivic cobordism recently found by Hopkins and Morel. For example, we compute the mod 2 motivic cohomology of a reduced Cech complex of a splitting variety according to Orlov, Vishik and Voevodsky. The cobordism ring $MGL / 2^{*,*} (Spec(\mathbb{R}))$ is computed and compared with the results of the real cobordism theory of Hu and Kriz. Moreover, we study algebraic cobordism of the classifying spaces $BG$ for algebraic groups over $\mathbb{C}$. For example, the Chow ring $CH^* (BG_2)_(2)$ for the exceptional Lie group $G_2$ is determined by using motivic cobordism and motivic cohomology.